On a Class of Bias-Amplifying Variables that Endanger Effect Estimates

TL;DR

This paper identifies and explains a class of variables, including instrumental variables, that can amplify confounding bias in causal effect estimation, especially in non-linear models, and discusses their impact on bias.

Contribution

The paper provides a simple derivation and intuitive explanation of bias amplification by certain variables, extending the analysis to non-linear models and clarifying their effects.

Findings

Instrumental variables can amplify bias in non-linear models.

Conditioning on instrumental variables may introduce new bias.

Instrumental variables do not affect selection-induced bias.

Abstract

This note deals with a class of variables that, if conditioned on, tends to amplify confounding bias in the analysis of causal effects. This class, independently discovered by Bhattacharya and Vogt (2007) and Wooldridge (2009), includes instrumental variables and variables that have greater influence on treatment selection than on the outcome. We offer a simple derivation and an intuitive explanation of this phenomenon and then extend the analysis to non linear models. We show that: 1. the bias-amplifying potential of instrumental variables extends over to non-linear models, though not as sweepingly as in linear models; 2. in non-linear models, conditioning on instrumental variables may introduce new bias where none existed before; 3. in both linear and non-linear models, instrumental variables have no effect on selection-induced bias.